%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SET912+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:39:20 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET912+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n002.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 03:12:06 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.47 Command-line arguments: --no-flatten-goal
% 0.17/0.47
% 0.17/0.47 % SZS status Theorem
% 0.17/0.47
% 0.17/0.47 % SZS output start Proof
% 0.17/0.47 Axiom 1 (commutativity_k3_xboole_0): set_intersection2(X, Y) = set_intersection2(Y, X).
% 0.17/0.47 Axiom 2 (commutativity_k2_tarski): unordered_pair(X, Y) = unordered_pair(Y, X).
% 0.17/0.47 Axiom 3 (t53_zfmisc_1): in(c, b) = true.
% 0.17/0.47 Axiom 4 (t53_zfmisc_1_1): in(a, b) = true.
% 0.17/0.47 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.17/0.47 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.17/0.47 Axiom 7 (t28_xboole_1): ifeq2(subset(X, Y), true, set_intersection2(X, Y), X) = X.
% 0.17/0.47 Axiom 8 (t38_zfmisc_1): ifeq(in(X, Y), true, ifeq(in(Z, Y), true, subset(unordered_pair(Z, X), Y), true), true) = true.
% 0.17/0.47
% 0.17/0.47 Goal 1 (t53_zfmisc_1_2): set_intersection2(unordered_pair(a, c), b) = unordered_pair(a, c).
% 0.17/0.47 Proof:
% 0.17/0.47 set_intersection2(unordered_pair(a, c), b)
% 0.17/0.47 = { by axiom 1 (commutativity_k3_xboole_0) }
% 0.17/0.47 set_intersection2(b, unordered_pair(a, c))
% 0.17/0.47 = { by axiom 2 (commutativity_k2_tarski) }
% 0.17/0.47 set_intersection2(b, unordered_pair(c, a))
% 0.17/0.47 = { by axiom 1 (commutativity_k3_xboole_0) R->L }
% 0.17/0.47 set_intersection2(unordered_pair(c, a), b)
% 0.17/0.47 = { by axiom 5 (ifeq_axiom) R->L }
% 0.17/0.47 ifeq2(true, true, set_intersection2(unordered_pair(c, a), b), unordered_pair(c, a))
% 0.17/0.48 = { by axiom 8 (t38_zfmisc_1) R->L }
% 0.17/0.48 ifeq2(ifeq(in(c, b), true, ifeq(in(a, b), true, subset(unordered_pair(a, c), b), true), true), true, set_intersection2(unordered_pair(c, a), b), unordered_pair(c, a))
% 0.17/0.48 = { by axiom 3 (t53_zfmisc_1) }
% 0.17/0.48 ifeq2(ifeq(true, true, ifeq(in(a, b), true, subset(unordered_pair(a, c), b), true), true), true, set_intersection2(unordered_pair(c, a), b), unordered_pair(c, a))
% 0.17/0.48 = { by axiom 6 (ifeq_axiom) }
% 0.17/0.48 ifeq2(ifeq(in(a, b), true, subset(unordered_pair(a, c), b), true), true, set_intersection2(unordered_pair(c, a), b), unordered_pair(c, a))
% 0.17/0.48 = { by axiom 4 (t53_zfmisc_1_1) }
% 0.17/0.48 ifeq2(ifeq(true, true, subset(unordered_pair(a, c), b), true), true, set_intersection2(unordered_pair(c, a), b), unordered_pair(c, a))
% 0.17/0.48 = { by axiom 6 (ifeq_axiom) }
% 0.17/0.48 ifeq2(subset(unordered_pair(a, c), b), true, set_intersection2(unordered_pair(c, a), b), unordered_pair(c, a))
% 0.17/0.48 = { by axiom 2 (commutativity_k2_tarski) }
% 0.17/0.48 ifeq2(subset(unordered_pair(c, a), b), true, set_intersection2(unordered_pair(c, a), b), unordered_pair(c, a))
% 0.17/0.48 = { by axiom 7 (t28_xboole_1) }
% 0.17/0.48 unordered_pair(c, a)
% 0.17/0.48 = { by axiom 2 (commutativity_k2_tarski) R->L }
% 0.17/0.48 unordered_pair(a, c)
% 0.17/0.48 % SZS output end Proof
% 0.17/0.48
% 0.17/0.48 RESULT: Theorem (the conjecture is true).
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